Bi-linear reduced-order models of structures with friction intermittent contacts

The dynamic analysis of structures with localized nonlinearities, such as intermittent contacts of cracked structures, is a computationally demanding task because of the large size of the models involved. Thus, high-resolution finite element models are often reduced using a variety of specialized techniques which exploit spatial coherences in the dynamics. In addition, when a steady-state forced response analysis is performed, direct time integration can be replaced with multi-harmonic balance methods. Recently, a technique based on bi-linear normal modes has been successfully applied to piecewise-linear oscillators. The key idea of that approach is to represent the spatial coherences in the system dynamics with two sets of normal modes with special boundary conditions, referred to as bi-linear modes. In this paper, the bi-linear modal representation is extended to the case of intermittent contacts with friction. Furthermore, a novel reduced order modeling method is developed for the 0th order harmonic used in multi-harmonic balance methods. The forced response of a cracked structure is used to demonstrate the proposed methods.